An adaptive multigrid solver for DPG methods with applications in linear acoustics and electromagnetics

We propose an adaptive multigrid preconditioning technology for solving linear systems arising from Discontinuous Petrov–Galerkin (DPG) discretizations. Unlike standard multigrid techniques, this preconditioner involves only trace spaces defined on the mesh skeleton, and it is suitable for adaptive...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2021-04, Vol.87 (na), p.12-26
Main Authors: Petrides, Socratis, Demkowicz, Leszek
Format: Article
Language:English
Subjects:
Acoustics
Adaptive systems
DPG methods
Finite element method
Grid refinement (mathematics)
hp-adaptivity
Linear systems
MATHEMATICS AND COMPUTING
Multigrid methods
Preconditioners for high-frequency wave propagation
Preconditioning
Solvers
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Summary:We propose an adaptive multigrid preconditioning technology for solving linear systems arising from Discontinuous Petrov–Galerkin (DPG) discretizations. Unlike standard multigrid techniques, this preconditioner involves only trace spaces defined on the mesh skeleton, and it is suitable for adaptive hp-meshes. The key point of the construction is the integration of the iterative solver with a fully automatic and reliable mesh refinement process provided by the DPG technology. The efficacy of the solution technique is showcased with numerous examples of linear acoustics and electromagnetic simulations, including simulations in the high-frequency regime, problems which otherwise would be intractable. Finally, we analyze the one-level preconditioner (smoother) for uniform meshes and we demonstrate that theoretical estimates of the condition number of the preconditioned linear system can be derived based on well established theory for self-adjoint positive definite operators.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2021.01.017